Theorems · Theorem · general topology
edist_lt_top
∀ {α : Type u_3} [inst : PseudoMetricSpace α] (x y : α), edist x y < ⊤In a pseudometric space, the extended distance is always finite
- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement · cited by 9,879
- Top.topstatement · cited by 9,680
- PseudoMetricSpacestatement and proof · cited by 1,550
- EDist.ediststatement · cited by 735
- edist_distproof · cited by 39
- ENNReal.ofReal_lt_topproof · cited by 22
Cited by32
Results whose statement or proof uses this declaration.
- edist_ne_topproof · cited by 17
- NormedSpace.exp_add_of_commuteproof · cited by 8
- NormedSpace.map_expproof · cited by 7
- MemHolder.holderWithproof · cited by 7
- Metric.eball_topproof · cited by 7
- NormedSpace.expSeries_div_hasSum_expproof · cited by 5
- hasDerivAt_exp_smul_constproof · cited by 3
- NormedSpace.exp_analyticproof · cited by 2
- NormedSpace.isUnit_expproof · cited by 1
- hasStrictDerivAt_expproof · cited by 1
- NormedSpace.norm_expSeries_div_summableproof · cited by 1
- NormedSpace.norm_expSeries_summableproof · cited by 1